Kyoto FDEPS lectures 4-7 xi 2007 Dynamics of oceans and atmospheres P.B. Rhines University of Washington

• 1. rotating, stratified fluids: oceans and atmospheres – vorticity: a vector-tracer in classical homogeneous fluids • geostrophic adjustment, thermal wind • 2. wave dynamics: fundamentals, group velocity, energetics, ray theory • potential vorticity (PV) – vortex stretching, Prandtl’ s ratio, geography of PV • 3. Rossby waves • 4. instability => geostrophic turbulence; subtropical gyres: dynamics, jets and gyres • 5. meridional overturning circulations and the thermohaline circulation • 6. Seminar: subpolar climate dynamics observed from above and below: altimetry and Seagliders Texture

Andy Goldsworthy AGU, 2003 water evaporates from the Great Lakes when cold north winds blow over them. It soon condenses back into water, as cloud droplets which then rain or snow out…The lake water has become cloud, and then the cloud piles up as deep snow, downwind of the lakes. This is called ‘lake-effect snow’.

Erika Dan temperature section, 600N Labrador-Greenland-Rockall-Ireland warm, saline water moving Worthington+Wright, 1970 north from the subtropics

deep winter mixing, sensitive shallow continental shelf circulation (unresolved in CCMs) to upper ocean low-salinity deep overflows from Denmark Strait/I.S. Ridge waters Five Davis Strait Seaglider temperature sections showing Arctic cold water entering the Labrador Sea, have unprecedented spatial resolution Eriksen & Rhines UW boundary mixing/ entrainment upwelling

broad upwelling, yet much of it recirculates below the mixed layer Jets occur in rotating fluids for many reasons, here driven by thermal convection in a bowl-shaped basin. The jets in the lefthand image occur due to the very strong topographic PV gradient, at high rotation (low Rossby number). Condie & Rhines ‘Topographic Hadley Cells JFM 1994; Rhines ‘Jets’, CHAOS 1994.

Cold disk Cold disk

low rotation high rotation spatially homogeneous, density stratified rotating convection viewed from the side: note streaks show w ~ u in small plumes yet also mesoscale structure is present

mixed layer base

GFD lab Univ of Washington

potential vorticity and buoyancy are the fundamental field variables for circulation

(here in 4 box-ocean wind-driven simulations) Hallberg & Rhines Dev. in Geophysical Turbulence, R. Kerr Ed., 2000 Theta-S diagram for Atlantic ocean (Southern Ocean to subpolar North Atlantic) cylinder wake in a soap film

Marvin Rutger

textures of different dynamical variables Vorticity in a ‘classic’ non-rotating fluid Vortex lines move with the (ideal) fluid….A famous billboard in Times Square, New York, 1950s. Note the size of the vortex rings, which are real. vortex lines are ‘vector tracers’ that move with the fluid vorticity: teaching tornados

‘Levitated’ balls with strong vertical and horizontal shear layers contain radial/vertical viscous overturning

Tornado vortex-2

Vorticity and forces: I = ½∫ω x r dV or one-half the dipole moment of the vorticity field is equal to the ‘impulse’, or time- integrated force exerted on a fluid…2/3 of which appears as momentum change of the fluid in 3D (the actual number depends uncomfortably on the shape of the control volume, as it recedes to infinity).

(in 2D the expression for impulse, ‘½’ is absent, yet the momentum change in a 2D fluid is still ½ I, that is ½ ∫ω x r dV) r=position vector, ω=vorticity vector Saffman, Vortex Dynamics, CUP

the rest of the impulse exerts a pressure force on the fluid at a great distance; this confusion is resolved if the fluid is slightly compressible in which case all the impulse appears as momentum. dipole wakes in the wake of the Aleutian Islands express the force exerted on the mountain slopes Planetary Rotation: gives stiffness to the fluid, creates ‘tall’ flow structures In our discussion of vortex line tipping and stretching we can now replace vorticity ω by absolute vorticity ω + 2Ω: the planetary vorticity amplifier Rotating fluids are filled with ‘tall’ structures

Andy Jackson, WUN 2004 Influence of rotation I: The Earth’s inner solid core is visible in the magnetic field; note the two maxima of the normal non-dipole field

After Gubbins & Bloxham (1985) Morphology of magnetic field lines from numerical dynamo simulation (Glatzmaier & Roberts, 1995) Jets on Jupiter: a good place to think about tall structures vs.thin, gravitationally stable layered Earth atmosphere. Here a deep, non-hydrostatic numerical model allows structures to line up with the rotation axis.

(Heimpel, Aurnou & Wicht, Nature 10 Nov 2005) planetary rotation can organize the chaotic textures of turbulent flow into coherent structures

GFD lab Univ of Washington Maximenko et al 2005 The geopotential: potential function Φ for gravity and centrifugal rotation effects the geoid Φ: for a symmetric model of Earth’s gravity TheThe presencepresence ofof planetaryplanetary vorticityvorticity amplifiesamplifies effectseffects ofof lineline--stretching:stretching:

a ring of air moved 1000 km north gains westerly velocity of about 100 m sec-1 (for f=10-4sec-1) There is not enough energy available to utilize this mode: the Hadley cell is limited in north-south extent. Forces (eddy momentum flux from PV stirring) and non-symmetric circulation are required to support extensive meridional excursion. A 2mm glass cylinder is held vertically…at rest in the non-rotating frame…in a rotating fluid…

Its 3D turbulent wake generates cyclonic tall vortices (Cormac Flynn, GFD Lab, Univ. of Washington also see computer sims of Smith & Waleffe Phys Fl 99 Morize,Moisy & Ribaud, PhysFl 05)

cylinder removed, showing final barotropic cyclones Turbulent flows exhibit remarkable transformation between non-geostrophic and quasi-geostrophic flow, in both directions. Here, a 3D turbulent cylinder wake converts into a 2D field of cyclonic vortices. This is as if you inserted your finger in the fluid as it rotates rapidly. the surface of a rotating fluid, slightly moving ( Rossby number << 1)

Dynamic height along latitude 60N from surface to stratosphere (1000 HPa to 30 HPa) for days 1-100 in 1996

30 HPa

1000 HPa longitude 0 180 0 Ocean currents at 50W longitude southeast of the Gulf Stream, over 7 months, showing very similar structure throughout water column: a strong barotropic mode

each line is a horizontal current vector plotted with eastward flow pointing upward rotational stiffness is related to inertial waves (often wave motions express restoring forces that strongly effect steady circulations too). inertial oscillations viewed by the movement of the water surface (essentially a pressure field). geostrophic balance: the sea surface at the Gulf Stream Tom Rossby, Oleander project, adcp based geostrophic balance: the pressure field along north-south lines in the atmosphere; day 1 1996 and day 180 1996 blue: 500 HPa dynamic height red: sea-level pressure NCEP reanalysis data steady, non-dissipative flows have a powerful Bernoulli function conservation principle: both the pressure variation along a streamline and across streamlines is known from the velocity field. • example: 2-dimensional flow around a circular cylinder. Adding rotation simply adds a pressure field that is a function of ψ. This shows how geostrophic flow has pressure gradient nearly perpendicular to the velocity, yet always with important pressure variations along streamlines 2D flow around a circular cylinder

Fig. The flow field (ψ) is at upper right. The pressure field for different values of the Rossby number, Ro = ∞, 3.3 and 1.1 • The pressure field for flow round a cylinder in a single-layer rotating fluid, at moderate Rossby number is simply the pressure for a non-rotating flow plus a function of ψ buoyancy: it’s tricky Geostrophic adjustment: initial value problem that ends up as a geostrophic flow

geostrophic adjustment: scenes from the North Pacific subtropical front region: Gregg, Brainerd, Hosegood, Alford

Velocity spirals: thermal wind balance one year current records at 2000, 3000, 3800m depth in the deep western boundary current

Stommel’s cooling spiral at OWS Juliette (52.5N, 20W) is a symptom of upward Qnet

Plot of (u,v) velocity components with depth as a parameter from hydrographic data Stommel, PNAS 1979 rotating and stratified flows..over simple mountains

Waves

Digital cameras readily do time-exposure streak images of particle paths (Nikon Coolpix 950) group velocity theory: stationary phase integral

Moiré patterns and group velocity

OSB In very shallow water, undular bores occur with both gravity- and capillary nature (backward and forward of the bore front, respectively); here in a 5m channel.

Knight Inlet, BC Undular bore and downslope jet forced by rapid tidal flow over a bank

David Farmer, IOS/URI

The table rotation rate is oscillated about its mean value to excite waves, with a small mountain. Fast, long hydrostatic Kelvin waves ans short non-hydrostatic inertial waves. 1 m diameter cylinder, GFD Lab Univ of Washington Kelvin waves, inertial waves in shallow rotating fluid internal gravity waves: rays and modes Jim Renwick, GFD lab Univ of Washington Waves: modes and rays and wave/mean-flow interaction at the base of the mixed layer

internalinternal gravitygravity waveswaves drivendriven byby oscillatingoscillating 22 dimensionaldimensional cylinder.cylinder. ViewedViewed withwith shadowgraphshadowgraph NoticeNotice reflectionreflection atat basebase ofof mixedmixed layerlayer GFD Lab, Univ of Washington frequency close to N..some generation of harmonics and some turbulent mixing internal gravity waves: a circular cylinder moves to the right steadily, horizontally notice the fluid which is pushed ahead of the cylinder, with too little kinetic energy to rise against the stratification. In a reference frame moving with the ‘mountain’ this would be blocked fluid upstream of the mountain. It is transmitted by long, low frequency gravity waves, visible in previous slide

geostrophic adjustment in a cylinder with 2 –layer stratification. A ball of fluid is injected at the interface and allowed to ‘slump’ and spin. Shall we try this during the lecture?

Rossby waves (barotropic mode) evolving in x and time (left); dispersion relation (right)

Rossby wave Green function for an oscillating vorticity source at the origin: with free-surface divergence barotropic Rossby waves excited by uniform westerly (eastward) zonal flow past a cylindrical mountain (McCartney JFM 1975)

Subtropical gyre dynamics, thermo- dyanamics and biology

Palter, Lozier & Barber Nature 2005 Oschlies, Williams, Garcon Follows, Nature Migillicuddy 1998 Nature 1998

TABLE OF CONTENTS • Polar amplification of the two 20th C warming events • Storms and weather….ocean to stratosphere: continuity of the Atlantic storm track/Icelandic Low from subtropics to high Arctic • Atmospheric and oceanic transports, strongly coupled, supply continental and polar warmth, fresh water • The oceanic heat source: northward heat transport essential to wintertime driving of 3 scales of atmospheric circulation, • Transports by ocean circulation: connecting the Arctic and Atlantic – Erika Dan, 600N winter in the N Atlantic: deep, shallow and shelf water masses – Atlantic – Arctic exchange: Θ-S-transport (~heat, fresh-water transport) diagrams – Rapid and slow modes of response of Atlantic overturning: Labrador Sea vs. Nordic Sea overflows – What matters to the global overturning circulation: • The freshwater cap and its movement: liquid and solid • Layering of deep-ocean water masses, and its representation in models • Shallow continental shelves and communication with the deep ocean • Arrays and instruments: establishing the baseline and sustaining it in time Global surface temperature has seen two major warmings in the 20th Century: in the 1920s-30s, when it was very concentrated around Greenland, and since the 1980s, when it is much more global, yet still concentrated in high northern latitudes.

Cod and herring fisheries responded to the much warmer ocean temperatures, which lasted for more than 25 years.

Ironically we anticipate the ocean circulation slowing during the current warming, whereas it is possible that an accelerated oceanic meridional overturning circulation was a factor in driving the 1920s warming. Surface Air Temperature Delworth+Knutson, Nature 1999

Uppernavik, West Greenland SAT anomaly (Imke Durre) The standing-wave structure with wintertime Icelandic and Aleutian Lows gives the atmosphere some of the east-west structure and gyre circulation familiar to the ocean. The rapid radiative cooling in fall sets up a cold dome which slumps under gravity, tending to create a surface polar vortex which is anticyclonic, the convergence overhead strengthening the polar cylonic vortex…yet mountains and vertical momentum transport can intervene, opposing the surface high.

In particular, the Atlantic storm-track forms a continuous connection between subtropics and the high Arctic. Lau’s JAS 1979 winter diabatic heating of the 700mb-1000mb lower atmosphere. Peak values are 100-150 watts/m2 in the subtropical storm track regions Held et al. (J.Clim.02) 100mb-1000mb diabatic heating for January Qnet, net atmosphere-ocean heat flux, watts/m2 (Keith Tellus 95) (annual average)

It should be noted that because the sun heats the ocean, O, but does not cool the atmosphere, A, the most useful maps of Qnet for A will differ those for O by the short-wave insolation. (from Thompson+Wallace J Clim 2000) 30 year trend in advection of time-averaged winter temperature (925-500 Hpa av.) ..anomalous velocity and advection, cooling the ocean while warming the land in both Atlantic and Pacific sectors. Could these oceanic advective heat sources be the root cause of this contribution to global warming over Eurasia? UT∂ / ∂x Hudson Strait salinity at 50m August 1965 (J.Lazier) This is part of the only 3-dimensional hydrographic survey ever made of the Labrador/Irminger seas.

Cuny et al. 2003 Northward moving Greenland shelf water Southward Irminger moving low- Current water salinity water circumnavigating from Baffin Bay the Labrador Sea The solution? Instrument the Arctic Rim. Do ASOF. Deploy the Eriksen Seaglider:

THE END

An evacuated glass vessel with water in it illustrates the Clausius-Clapyron relation between vapor pressure of water and temperature. The water is pushed from the vessel in my hand to the ‘cold ball’, and the vapor pressure difference between the two ends is close to the hydrostatic pressure measured by the column’s vertical displacement. One can fill out the curve and see the greater sensitivity (to temperature) of water vapor production at high, ‘tropical’ temperature. This all works because we shake the vessel so that a thin film of water lies under my warm hand. It illustrates a key variable in the climate system. When shaken this water ‘clinks’ like metal,vapor cavities opening up and slamming shut. Ocean advection, Arctic-Atlantic Connections, Climate P.B.Rhines, University of Washington Sirpa Hakkinen, NASA Goddard SPC with David Bailey, Wei Cheng, Jerome Cuny, Trisha Sawatzky WUN Climate teleseminar, 26iii2003

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www.ocean.washington.edu /research/gfd/gfd.html • FDEPS Lectures, November 2007 • P.B. Rhines, Oceanography and Atmospheric Sciences, University of Washington • [email protected] • www.ocean.washington.edu/research/gfd • • These lectures will address the dynamics of oceans and atmospheres, as seen through theory, laboratory simulation and field observation. We will look particularly at high latitudes and climate dynamics of the ocean circulation coupled to the atmospheric storm tracks. We will emphasize the dynamics that is difficult to represent in numerical circulation models. We will discuss properties of oceans and atmospheres that are both fundamental, unsolved questions of physics, and are also important, unsolved problems of global environmental change. • Lecture 1: • Is the ocean circulation important to global climate ? Does dense water drive the global conveyor circulation? Fundamental questions about oceans and atmospheres that are currently under debate. • • The field theory for buoyancy and potential vorticity. • Basic propagators: Rossby waves and geostrophic adjustment. • Potential vorticity: inversion and flux. • Lecture 2: • How do waves and eddies shape the general circulation, gyres and jet streams? • Almost invisible overturning circulations. • Lessons from Jupiter and Saturn. • The peculiar role of mountains, seamounts and continental-slope topography. • Lecture 3: • Dynamics of ocean gyres and their relation with the global conveyor circulation. • Water-mass transport, transformation and air-sea exchange of heat and fresh water. • Ocean overflows and their mixing. • Decadal trends in the global ocean circulation. • Lecture 4: • Heat, fresh-water, ice: convection in oceans and atmospheres and the texture of geophysical fluids. • Lecture 5: • Teaching young students about the global environment using the GFD laboratory: science meets energy and environment in the lives of Arctic natives • Seminar: • Exploring high-latitude ocean climate with Seagliders and satellites